Friday, May 2, 2014

Random “Guessing”

Today in Statistics, we investigated the following scenario:

A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 13. For each question left unanswered, the score is 4. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?1

I gave students about 20 minutes to tackle this question (along with another probability question) in groups. The following was a humorous exchange I overheard:

Guy: It might be 4 choices…
Girl: Uh… If you can eliminate 4 choices, then you’re not guessing!

Of course, the practical analogy is the SAT, on which students earn 1 point for each correct response, and lose 0.25 points for each incorrect response (while netting zero points for every question they skip).2

Based on the earlier exchange, I felt the need to emphasize:

Yeah, if you can eliminate 4 choices on an SAT question, then you should DEFINITELY answer the question.

  1. If you’re curious, the answer is: Two choices. []
  2. At least until Spring 2016, when College Board eliminates the penalty for incorrect responses on the SAT. []